On Feb 4, 5:00*pm, (Edward A. Falk) wrote:
To solve this puzzle, you need to ask how the control system works.

Method #1: *A device attached to the vehicle monitors the speed of the
wheels and transmits this to the conveyor belt's control system which
runs the belt in the opposite direction at the same speed.

Method #2: *Some sort of position-detecting system observes the vehicle's
position on the belt, and feeds back to a servo system that increases
the belt's backwards speed if the vehicle starts making forward progress,
or decreases it if the vehicle starts sliding backwards.

(Someone want to propose a different control system?)

Both systems are actually equivalent in their effects on automobiles
and airplanes.

An automobile is held in position no matter what the driver attempts
to do.

With airplanes, the situation is different. *Because the plane has
free-wheeling wheels, and doesn't depend on pushing against the belt in
order to move forward, it begins to make progress.

At this point, the belt -- which is a perfect conveyor belt -- instantly
speeds up to infinite speed. *The airplane's wheels -- which are perfect
wheels -- likewise instantly spin up to infinite speed. *Since the wheels
are perfect and have no friction, the airplane is not affected and takes
off anyway.

If you don't assume perfect abstractions, then the answer depends on
what happens first: *Either a) the belt reaches its upper speed limit
and the plane takes off, b) the plane's bearing seize and the plane is
flung backwards off the belt, or c) the breeze caused by friction between
the belt and the atmosphere is sufficient for the plane to take off
before a) or b) happens.

--
* * * * -Ed Falk,
* * * *http://thespamdiaries.blogspot.com/

Well, if you are going to start inserting idealized and impossible
conditions, then lets say that the wheels are also ideal and generate
no friction. In that case, the plane will still take off because the
wheels impart no force whatsoever on the airplane...